Question
A body of mass m is placed on the rough inclined plane of inclination θ. Coefficient of friction of surface is μ. What is the work done to take the body up the inclined plane against friction by distance S?
Solution
Let a body of mass m be placed on a rough inclined plane and displaced from A to B by a distance S, as shown in the fig.
Now, breaking force into it's rectangular components,
(i) mg sinθ is the component down the inclined plane.
Now, breaking force into it's rectangular components,
(i) mg sinθ is the component down the inclined plane.
(ii) mgcosθ is the component perpendicular to plane.
Since body is in equilibrium perpendicular to the plane,
Since the body is displaced up the inclined plane, therefore force of friction will be down the inclined plane.
Force of friction, 
∴ Work done against friction is,
